Answer
The solution is $\Big[-\dfrac{2}{3},4\Big]$
Work Step by Step
$|5-3x|\le7$
Solving this absolute value inequality is equivalent to solving the following inequality:
$-7\le5-3x\le7$
$\textbf{Solve the inequality shown above:}$
$-7\le5-3x\le7$
Subtract $5$ from all three parts of the inequality:
$-7-5\le5-5-3x\le7-5$
$-12\le-3x\le2$
Divide all three parts of the inequality by $-3$ and reverse the inequality signs:
$\dfrac{-12}{-3}\ge\dfrac{-3x}{-3}\ge-\dfrac{2}{3}$
$4\ge x\ge-\dfrac{2}{3}$
Expressing the solution in interval notation:
$\Big[-\dfrac{2}{3},4\Big]$
